A novel asymptotic formulation for partial slip half-plane frictional contact problems

Abstract

A method of solution and the necessary calibrations are given to permit the steady-state extent of slip to be found in contacts properly described within a half-plane formulation using only two parameters: the contact law and the first-order descriptions of tractions arising at the contact edges. The approach takes the assumption of full stick and corrects for the slip regions using an array of glide dislocations. This is a very versatile approach and is particularly appropriate when studying fretting fatigue, as it permits the region in which cracks nucleate to be defined very simply, and in a form which is transportable from contact to contact, including laboratory tests. The approach has the additional benefit of giving a relatively straightforward expression for the density of dislocations, from which the slip displacement and shear traction within the stick region may readily be calculated. An example implementation is provided in the case of a Hertzian contact in the absence of changes in bulk tension, for which we demonstrate the veracity of the predictions by comparing to previous asymptotic approaches that build upon the traction solution under the assumption of full sliding, as well as the known exact solution.